Although Byas insisted he is working flat out to strengthen a squad that came third-bottom of last season's Second Division, and that Yorkshire are in discussion with a number of potential targets, he said it was proving "extremely difficult" to find quality performers of established pedigree.
With the exception of cricketers such as Alex Tudor, the former England fast bowler released by Surrey following a spate of injury problems, there is a paucity of well-known players available.
Byas intimated Yorkshire were more likely to go for lesser-known players of untapped potential, possibly even from the local leagues, but stressed he would not be panicked into recruiting cricketers "just for the sake of it."
He said: "I know some people will be expecting us to make big-name signings, but there are not many of those players around.
"It's not even a question of money. We haven't got the resources to go around throwing money at players in an effort to bring them to Headingley, but even if we did have those funds, there is a lack of established, quality cricketers available at the present time, so cash needn't necessarily come into the equation in any case.
"Any county worth its salt has its best players under contract, as we have at Yorkshire.
"I suppose the reality is that we're trying to recruit big-performing cricketers as opposed to what you would call big-name cricketers, but, as I've already said, we will only sign players if they are absolutely right for the club, not because of any need for us to sign players full stop."
Byas, anxious to boost a seam bowling department that has been worryingly short of form and depth, said: "I would certainly consider players from the leagues, be they from the Yorkshire leagues or from a league elsewhere in the country.
"Again, there are not exactly a large number of cricketers who would fit the bill in that respect, but if someone did come to our attention and we liked the look of them we would certainly take a closer look at the situation.
"The search is on-going and it's not proving easy, but at the same time I'm relatively confident that we will go into next season with a couple of new additions and, consequently, that we will be able to boost competition for places, which is absolutely vital."
Yorkshire fast bowler Chris Silverwood has successfully undergone an ankle operation.
Silverwood missed nine championship matches last season through a combination of foot, heel and ankle difficulties.
"The doctors detected a small bone growth about the size of the end of a thumb which was catching somewhere in Chris's ankle," said Byas. "It had been causing him a lot of discomfort, but, touch wood, he should be back bowling in the nets around December."
Byas acknowledged some Yorkshire supporters would nevertheless be concerned that Silverwood and Craig White, the captain, who has also experienced long-standing injury problems, might struggle to withstand the rigours of a full campaign.
White, reappointed leader for 2005, missed the final 17 games of last season after going down with a knee injury in the Twenty20 Cup match against Lancashire and bowled only 88.2 overs in championship cricket.
"Both players have had problems with injuries, but I'm confident we will see a lot more of them next year," added Byas.
"Craig's injury last year was freakish in that he managed to tear a muscle in innocuous fashion while fielding, while Chris's problem has been rectified by surgery, so I'm not unduly worried about the situation.
"Craig is back to full fitness and getting him and Chris on the park will be like having two new signings.
"Both are proven performers with the ball and could make a heck of a difference in 2005."
chris.waters@ypn.co.uk